91Ó°ÊÓ

The number of cell telephone subscribers in the United States from \(1995-2010\) can be modeled by \(f(x)=25 x^{23 / 25},\) where \(f(x)\) is the number of cellular telephone subscriptions in millions, \(x\) years after \(1995 . \text { (Source: CTIA-Wireless Association, } 1995-2010)\) Use this information to answer. Explain how writing \(2 x^{-5}\) with positive exponents is similar to writing \(2 x^{-3 / 4}\) with positive exponents.

Simplify. See a Concept Check in this section. Assume variables represent positive numbers. $$ \sqrt[4]{a^{12} b^{4} c^{20}} $$

Fill in each box with the correct expression. $$ \square \cdot a^{2 / 3}=a^{3 / 3}, \text { or } a $$

Fill in each box with the correct expression. $$ \square \cdot x^{1 / 8}=x^{4 / 8}, \text { or } x^{1 / 2} $$

Simplify. See a Concept Check in this section. Assume variables represent positive numbers. $$ \sqrt[3]{a^{9} b^{21} c^{3}} $$

Simplify. See a Concept Check in this section. Assume variables represent positive numbers. $$ \sqrt[3]{z^{32}} $$

Fill in each box with the correct expression. $$ \frac{\square}{x^{-2 / 5}}=x^{3 / 5} $$

Simplify. See a Concept Check in this section. Assume variables represent positive numbers. $$ \sqrt[5]{x^{49}} $$

Fill in each box with the correct expression. $$ \frac{\square}{y^{-3 / 4}}=y^{4 / 4}, \text { or } y $$

Use a calculator to write a four-decimal-place approximation of each number. $$ 8^{1 / 4} $$